Extract code-mode nested tool collection into codex-tools (#16509)

## Why
This is another small step in the `codex-core` -> `codex-tools`
migration described in `AGENTS.md`.

`core/src/tools/spec.rs` and `core/src/tools/code_mode/mod.rs` were both
hand-rolling the same pure transformation: convert visible `ToolSpec`s
into code-mode nested tool definitions, then sort and deduplicate by
tool name. That logic does not depend on core runtime state or handlers,
so keeping it in `codex-core` makes `spec.rs` harder to peel out later
than it needs to be.

## What Changed
- Add `collect_code_mode_tool_definitions()` to
`codex-rs/tools/src/code_mode.rs`.
- Reuse that helper from `codex-rs/core/src/tools/spec.rs` when
assembling the `exec` tool description.
- Reuse the same helper from `codex-rs/core/src/tools/code_mode/mod.rs`
when exposing nested tool metadata to the code-mode runtime.

This is intended to be a straight refactor with no behavior change and
no new test surface.

## Verification
- `cargo test -p codex-tools`
- `cargo test -p codex-core tools::spec::tests`
- `cargo test -p codex-core code_mode_only_`

codex-rs/core/src/tools/code_mode/mod.rs

@@ -28,7 +28,7 @@ use crate::tools::router::ToolRouterParams;
 use crate::unified_exec::resolve_max_tokens;
 use codex_features::Feature;
 use codex_tools::ToolSpec;
-use codex_tools::tool_spec_to_code_mode_tool_definition;
+use codex_tools::collect_code_mode_tool_definitions;
 use codex_utils_output_truncation::TruncationPolicy;
 use codex_utils_output_truncation::formatted_truncate_text_content_items_with_policy;
 use codex_utils_output_truncation::truncate_function_output_items_with_policy;
@@ -244,14 +244,8 @@ pub(super) async fn build_enabled_tools(
     exec: &ExecContext,
 ) -> Vec<codex_code_mode::ToolDefinition> {
     let router = build_nested_router(exec).await;
-    let mut out = router
-        .specs()
-        .into_iter()
-        .filter_map(|spec| tool_spec_to_code_mode_tool_definition(&spec))
-        .collect::<Vec<_>>();
-    out.sort_by(|left, right| left.name.cmp(&right.name));
-    out.dedup_by(|left, right| left.name == right.name);
-    out
+    let specs = router.specs();
+    collect_code_mode_tool_definitions(&specs)
 }
 
 async fn build_nested_router(exec: &ExecContext) -> ToolRouter {

codex-rs/core/src/tools/spec.rs

@@ -29,6 +29,7 @@ use codex_tools::ViewImageToolOptions;
 use codex_tools::WaitAgentTimeoutOptions;
 use codex_tools::WebSearchToolOptions;
 use codex_tools::augment_tool_spec_for_code_mode;
+use codex_tools::collect_code_mode_tool_definitions;
 use codex_tools::collect_tool_search_app_infos;
 use codex_tools::collect_tool_suggest_entries;
 use codex_tools::create_apply_patch_freeform_tool;
@@ -72,7 +73,6 @@ use codex_tools::dynamic_tool_to_responses_api_tool;
 use codex_tools::mcp_tool_to_responses_api_tool;
 use codex_tools::request_permissions_tool_description;
 use codex_tools::request_user_input_tool_description;
-use codex_tools::tool_spec_to_code_mode_tool_definition;
 use std::collections::HashMap;
 
 #[cfg(test)]
@@ -202,13 +202,14 @@ pub(crate) fn build_specs_with_discoverable_tools(
             dynamic_tools,
         )
         .build();
-        let mut enabled_tools = nested_specs
-            .into_iter()
-            .filter_map(|spec| tool_spec_to_code_mode_tool_definition(&spec.spec))
-            .map(|tool| (tool.name, tool.description))
-            .collect::<Vec<_>>();
-        enabled_tools.sort_by(|left, right| left.0.cmp(&right.0));
-        enabled_tools.dedup_by(|left, right| left.0 == right.0);
+        let enabled_tools = collect_code_mode_tool_definitions(
+            nested_specs
+                .iter()
+                .map(|configured_tool| &configured_tool.spec),
+        )
+        .into_iter()
+        .map(|tool| (tool.name, tool.description))
+        .collect::<Vec<_>>();
         push_tool_spec(
             &mut builder,
             create_code_mode_tool(&enabled_tools, config.code_mode_only_enabled),

codex-rs/tools/src/code_mode.rs

@@ -37,6 +37,18 @@ pub fn tool_spec_to_code_mode_tool_definition(spec: &ToolSpec) -> Option<CodeMod
         .then(|| codex_code_mode::augment_tool_definition(definition))
 }
 
+pub fn collect_code_mode_tool_definitions<'a>(
+    specs: impl IntoIterator<Item = &'a ToolSpec>,
+) -> Vec<CodeModeToolDefinition> {
+    let mut tool_definitions = specs
+        .into_iter()
+        .filter_map(tool_spec_to_code_mode_tool_definition)
+        .collect::<Vec<_>>();
+    tool_definitions.sort_by(|left, right| left.name.cmp(&right.name));
+    tool_definitions.dedup_by(|left, right| left.name == right.name);
+    tool_definitions
+}
+
 pub fn create_wait_tool() -> ToolSpec {
     let properties = BTreeMap::from([
         (

codex-rs/tools/src/lib.rs

@@ -42,6 +42,7 @@ pub use apply_patch_tool::ApplyPatchToolArgs;
 pub use apply_patch_tool::create_apply_patch_freeform_tool;
 pub use apply_patch_tool::create_apply_patch_json_tool;
 pub use code_mode::augment_tool_spec_for_code_mode;
+pub use code_mode::collect_code_mode_tool_definitions;
 pub use code_mode::create_code_mode_tool;
 pub use code_mode::create_wait_tool;
 pub use code_mode::tool_spec_to_code_mode_tool_definition;